26
DIFFERENCE
IN
POTENTIALS
quantities
ca
that pertain
to
the
atoms constituting
the liquid molecules.
This,
too,
opens ample
possibilities for testing
the
theory inasmuch
as
the
cQ
can
be
arbitrarily overdetermined.
Here, too,
the result
must
be
independent
of the choice
of
the metal ions.
§7.
Calculation
of (r2-r1)
All that
now
remains
is
to
study
the diffusion
process
in
the
space
V
in
greater
detail.
Let
the variable
quantities
depend
on z
only,
where
the
z-axis of the Cartesian coordinate
system
we
have
chosen
coincides with the
direction of the axis of
our
vessel.
vm1
, vs1 ,
vm2
,
and
vs2
shall
be
the
z-dependent
concentrations
(gram-equivalents
per
unit
volume)
of the four
ionic
species,
em1E, -es1E,
em2E,
-es2E
their electric
charges,
and
r
the
electric
potential.
Since
no
substantial electric
charges
occur
anywhere,
we
have
for all
z
approximately
(a)
v e
-
v e + v e
-
v e
=0
wx
Si
st
m2 m2
s2 s2
In
addition,
for
each
ionic
species
we
obtain
an
equation which states
that the increase
per
unit time in the
number
of
ions
of
a
certain kind
present
in
one
volume
element
equals
the difference
between
the
number
of
molecules
entering
and
the
number
of
molecules
leaving
that volume element
during
the
same
time
period:
[12]
iß)
dv
in
•L
{RT_/iI
+ =
7Jf
oil
S
+
...................
...................